A306867 Lesser of augmented bi-unitary amicable pair.

434784, 1100176, 1252216, 1754536, 2166136, 2362360, 3064096, 6224890, 7626136, 7851256, 7950096, 9026235, 9581320, 12494856, 13324311, 14192080, 15218560, 15243424, 15422536, 19028296, 19466560, 19555360, 29180466, 36716680, 37542190, 40682824, 44044000, 44588896

Offset

1,1

Comments

A pair m < n is an augmented bi-unitary amicable pair if bsigma(m) = bsigma(n) = m + n - 1, where bsigma(n) is the sum of bi-unitary divisors of n (A188999).

The larger members are in A306868.

Links

Amiram Eldar, Table of n, a(n) for n = 1..509 (terms below 2*10^11, from David Moews's site).

David Moews, Perfect, amicable and sociable numbers.

Example

434784 is in the sequence since it is the lesser of the amicable pair (434784, 871585): bsigma(434784) = bsigma(871585) = 1306368 = 434784 + 871585 - 1.

Mathematica

fun[p_, e_]:=If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); f[n_] := bsigma[n] - n + 1; s={}; Do[m = f[n]; If[m > n && f[m] == n, AppendTo[s, n]], {n, 1, 10^7}]; s

Crossrefs

Cf. A007992, A126174, A188999, A292980, A306868.

Sequence in context: A085092 A117151 A186048 * A163612 A238069 A234150

Adjacent sequences: A306864 A306865 A306866 * A306868 A306869 A306870

Keyword

nonn

Author

Amiram Eldar, Mar 14 2019

Status

approved